Moment based model predictive control for linear systems: Additive perturbations case

In this article, we present a novel linear model predictive control (MPC) strategy for controlling uncertain dynamical systems. The moment based MPC strategy is based on the (centralized) moments of the stochastic cost and constraint functions. We show that moment based MPC formulations yield computationally tractable predictive control problems, due to the explicit analytic expressions of the moments and linearity in the dynamics. This article considers (i) the output regulation MPC configuration, where the output is steered towards a reference and state vector is not correctly accessible to the controller at the decision instants; (ii) the moment based MPC formulation with uncertainties that are non-Gaussian random variables, and (iii) bound and polytopic constraints in the uncertain MPC problem subject to either Gaussian disturbances or uncertainties with symmetric distributions. We demonstrate the effectiveness of the proposed MPC technique on simulation examples such as a double integrator system and a quadruple tank system.